Investigating the classical and alternative vibration absorbers

Nowadays, undesirable vibrations are among the most important problems for machines and buildings such as skyscrapers, towers and bridges. Due to the vibrations, machines may operate more noisily and may lead to undesirable consequences. Also, these vibrations can cause loss of life and property if they occur in large structures such as bridge, building and towers. To avoid these undesirable vibrations, the vibrations that may occur in the future must be investigated and preventative measures should be taken to avoid or minimise such vibrations during the design stages of machines and structures. However, vibrations may take place on systems due to the unforeseen reasons or due to not being able to make, during the design stage, accurate estimations of the environments that structures operate. Such vibrations are frequently dealt with by using dynamic vibration absorber that can be added to the system later. The so-called Dynamic Vibration Absorber (DVA) is a single-degree-of-freedom system that consists of a mass, a spring and optionally a damper. DVA is frequently used to minimize the vibrations of machines and structures, simply by attaching it to the system and tuning it to the desired frequency. In the beginning of the twentieth century, the first DVA was designed only with a simple mass and a spring. After a while, it was started to be used as a tool for projection of buildings from wind and earthquake vibrations. It was used in mechanical devices to reduce the resonance vibrations. In line with the development of technology, new kinds of DVAs were investigated such as liquid dynamic mass dampers, magnetic dynamic vibration absorbers and cantilever beam vibration absorbers etc. These kinds of DVAs were named as "Passive vibration absorbers". Passive vibration absorbers have major disadvantages; one of the most important one is the ability to work in a narrow frequency band. Because of this, researchers and engineers are searching for new kinds of DVAs which can operate successfully at broad frequency bands. These types of DVA's are usually called as "adaptive dynamic vibration absorbers (ADVA)". During operation, ADVA can change stiffness of its components which is similar to adjustable spring such as magneto rheological elastomers and shape memory elements; and may also have ability to tune itself according to the operational environment. Within the scope of this master thesis; passive DVAs such as traditional (mass-spring), magnetic and gas DVAs' are investigated. The traditional DVA, which is a mass-spring system, is investigated on a washing machine under harmonic vibrations at 840 rpm and 1200 rpm, and its effectiveness is assessed by experimental approach. Before the experiments, traditional DVA system was designed without using dampers. Two masses, 1 kg and 2 kg, are used to assess the performance of traditional DVA design. The DVA with 1 kg mass was designed for 1200 rpm (20 Hz) and the one with 2 kg mass for 840 rpm (14 Hz). Traditional DVA had 3 attachment points, similar to the washing machine's upper balancing mass. First, experiments on washing machine were carried out without the DVA and vibrations measurements were made at steady state spinning speeds at 600, 800, 1000 and 1200 rpm. Then the upper balancing mass was removed and DVA system was attached to the tub. However, in order to make meaningful comparisons, the total mass of the DVA including its base was designed such that the total mass of the DVA was the same as that of the upper balancing mass of the washing machine. Vibration measurements were made to at the hub, demonstrating that the classical DVA can bring some vibration reduction at the tub. However, the disadvantages of the classical DVA were also obvious, major ones being very noisy operation, strength problems at the spring connections, highly stressed spring. For the purpose of eliminating the adverse mechanical effects due to mechanical spring, alternative systems that can store energy like a spring were investigated in this thesis. The repulsive force of the magnets and the pressure force that the compressed gases apply in the opposite direction of the compression were aimed to be modelled like spring forces in this thesis. For magnetic DVA, minimum three magnets must be used and the opposing poles of the magnets must be at the same magnetic polar. The reason behind this situation is that, there are 2 types of force, pulling and repelling, that can be generated between magnets. In magnetic DVA, the repelling force is to be used. Otherwise, the magnets will be attached to each other and stiffness behaviour will not be created. For the gas DVA, on the other hand, compressed gas is used as energy storage medium. When the gas is compressed, the gas pressure is increased. In this thesis, to design a gas DVA, two chambers and one mass, separating the two chambers from each other, is used. In this thesis, the repulsive forces of the MDVA and the pressure of the compressed gas of the gas DVA were calculated theoretically. It is clear that these forces in such systems are non-linear functions of the displacements, yielding a stiffness parameter which depends on displacement. Here, for a given level of harmonic vibration, an equivalent stiffness parameter is determined using Harmonic Balance Method. Discrete Fourier Transform is utilised for this purpose. The first studies were conducted on MDVA. Equivalent spring constant of the MDVA system was calculated as a function of the distance between magnets and the amplitude of vibration of the absorber mass. Then, by using equivalent spring constant, MDVA's natural frequency was calculated. In the light of these results, it is observed that the natural frequency of the system increases as the amplitude of vibration of the absorber mass increases and the natural frequency decreases as the distance between the magnets increases. Then, theoretical and experimental studies were carried out MDVA. Experimental measurements were performed to measure the natural frequency of the MDVA system and then experimental and theoretical results were compared. These comparisons verified the theoretical model and its predictions. It was then decided to implement the MDVA system on a cantilever beam. Frequency response functions of beam were measured on cantilever beam with and without the MDVA system. Results showed that, MDVA system is operating effectively, reducing vibrations around the tuned frequency. After the assessment of the MDVA system, Gas DVA system was investigated. First of all, as in the MDVA system, equivalent spring constant produced by gas DVA system was calculated. Equivalent stiffness of the gas DVA system was calculated as a function of the axial length the cylinder and the amplitude of the displacement of the absorber mass. Then, by using the equivalent stiffness, amplitude dependent gas DVA's natural frequency was calculated. The results show that natural frequency of the gas DVA system increases while the amplitude of displacement of the absorber mass increases. Moreover, as the axial length of the gas DVA is increased, the natural frequency of system is decreased. In subsequent studies, it was decided to design a Gas DVA and validate its natural frequency by experimental means. The designed gas DVA system consists of 2 equal cylindrical chambers which are separated by piston-like mass which acts as an absorber mass. The sealing property is very important for this system, which makes it very difficult to measure the vibrations of the absorber mass inside the cylinder. However, a simple 2 degrees-of-freedom mathematical model is developed for the gas DVA system including 2 masses and 1 spring with equivalent spring constant to calculate the natural frequency. Then, experimentally identified natural frequency (using the measurements on the cylinder block of gas DVA) is compared with analytically calculated natural frequency. The predicted behaviour of the gas DVA is found to be in perfect match with that of the measured behaviour. However, some differences in quantitative results are also noticed, possibly due to the additional stiffness caused by the wall friction and lubrication in the physical model, but not considered in the theoretical model. Additionally, viscous damping ratio was identified, using the measured data, to be approximately 5%. Then the gas DVA system was tested on a cantilever beam. Frequency response functions of the cantilever beam were measured at low levels of vibrations, with and without gas DVA. Results showed that, gas DVA system is behaving as expected, functioning effectively and reducing the vibrations levels around the tuned natural frequency very significantly. In this thesis; effectiveness of traditional, magnetic and gas DVAs were examined. It has been seen that the magnetic and gas DVA systems can be used instead of traditional DVA system. MDVA and gas DVA systems can be designed at high frequencies and may operate without some of the drawbacks of conventional DVA. Finally, it is worth stating that these alternative DVA systems are also more suitable for active vibration control applications.